SOLUTION: The sum of the measures of two obtuse angle is 215.The sum of three-fifths of the supplement of the smaller angle and two-thirds the supplement of the larger angle is 91. Find the

Algebra ->  Angles -> SOLUTION: The sum of the measures of two obtuse angle is 215.The sum of three-fifths of the supplement of the smaller angle and two-thirds the supplement of the larger angle is 91. Find the       Log On


   

Question 147652: The sum of the measures of two obtuse angle is 215.The sum of three-fifths of the supplement of the smaller angle and two-thirds the supplement of the larger angle is 91. Find the measure of the two angles.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two angels be a and b
a+b = 215
We are also given a second set of information
The supplement of an angle plus the angle is always 180.
We are told %283%2F5%29%2A%28180-a%29+%2B+%282%2F3%29%2A%28180-b%29+=+91
108+-+%283%2F5%29a+%2B+120+-+%282%2F3%29b+=+91
-%283%2F5%29a+-+%282%2F3%29b+=+-137
9a+%2B+10b+=+2055
Now solve using
9a+%2B+10b+=+2055
a+%2B+b+=+215
Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition


Lets start with the given system of linear equations

9%2Ax%2B10%2Ay=2055
1%2Ax%2B1%2Ay=215

In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).

So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.

So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 9 and 1 to some equal number, we could try to get them to the LCM.

Since the LCM of 9 and 1 is 9, we need to multiply both sides of the top equation by 1 and multiply both sides of the bottom equation by -9 like this:

1%2A%289%2Ax%2B10%2Ay%29=%282055%29%2A1 Multiply the top equation (both sides) by 1
-9%2A%281%2Ax%2B1%2Ay%29=%28215%29%2A-9 Multiply the bottom equation (both sides) by -9


So after multiplying we get this:
9%2Ax%2B10%2Ay=2055
-9%2Ax-9%2Ay=-1935

Notice how 9 and -9 add to zero (ie 9%2B-9=0)


Now add the equations together. In order to add 2 equations, group like terms and combine them
%289%2Ax-9%2Ax%29%2B%2810%2Ay-9%2Ay%29=2055-1935

%289-9%29%2Ax%2B%2810-9%29y=2055-1935

cross%289%2B-9%29%2Ax%2B%2810-9%29%2Ay=2055-1935 Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether.



So after adding and canceling out the x terms we're left with:

1%2Ay=120

y=120 Divide both sides by 1 to solve for y



y=120 Reduce


Now plug this answer into the top equation 9%2Ax%2B10%2Ay=2055 to solve for x

9%2Ax%2B10%28120%29=2055 Plug in y=120


9%2Ax%2B1200=2055 Multiply



9%2Ax=2055-1200 Subtract 1200 from both sides

9%2Ax=855 Combine the terms on the right side

cross%28%281%2F9%29%289%29%29%2Ax=%28855%29%281%2F9%29 Multiply both sides by 1%2F9. This will cancel out 9 on the left side.


x=95 Multiply the terms on the right side


So our answer is

x=95, y=120

which also looks like

(95, 120)

Notice if we graph the equations (if you need help with graphing, check out this solver)

9%2Ax%2B10%2Ay=2055
1%2Ax%2B1%2Ay=215

we get



graph of 9%2Ax%2B10%2Ay=2055 (red) 1%2Ax%2B1%2Ay=215 (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle).


and we can see that the two equations intersect at (95,120). This verifies our answer.


To get a = 95 and b = 120